A bicycle training device known as “bicycle rollers” has been available for over one hundred years. This device consists of three rollers supported by a frame. In use, the rear wheel of a bicycle is brought to rest on two, relatively closely spaced (by about 20 cm) bracketing rollers and the front wheel is balanced on top of the third roller. This device permits a user to balance and steer the bicycle (within a range) and to pedal at any speed desired. Unfortunately, users are constrained as to how aggressively they can exercise since rapid changes in pedaling speed and rider position can easily cause the rear wheel to pop out of its bracketing rollers. Additionally, a bicycle which is rigidly constrained acts to discourage the rider's natural movement and is somewhat uncomfortable to ride. It is a principle object of this invention to provide an additional degree of motion to more closely duplicate the natural feel of outdoor cycling.